How can I determine whether a car in a video is moving or not?
CNNs are translation invariant.

You are over complicating the problem.  The easiest thing you can do is define a region of interest (ROI) of the hood.  In the first case where the car is moving and the reflections are dynamic.  In the second case they are static.  Just do frame-to-frame image subtraction of the hood.  If the vehicle is moving you will have lots of 'edge energy'.  If it is not moving it will be just noise.  

You can apply the same method to the whole image too.  In the static case the image subtraction method may become messy as the clouds are moving along with vehicles and pedestrians.  For this case use the image subtractions as input to your method.

Another approach is to run an image stabilization algorithm.  OpenCV has one.  Look at the transformation outputs (translation, rotation, scale, rigid, similarity, affine, etc.).  If you can't make a simple filter on them to determine the two cases, train a classifier.